Supporting Information. Interfacial Shear Strength of Multilayer Graphene Oxide Films
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1 Supporting Information Interfacial Shear Strength of Multilayer Graphene Oxide Films Matthew Daly a,1, Changhong Cao b,1, Hao Sun b, Yu Sun b, *, Tobin Filleter b, *, and Chandra Veer Singh a, * a Department of Materials Science and Engineering, University of Toronto, 184 College St, Toronto, ON, Canada, M5S 3E4 b Department of Mechanical and Industrial Engineering, University of Toronto, 5 King s College Rd, Toronto, ON, Canada, M5S 3G8 *Corresponding authors 1. Atomic force microscopy (AFM) topographical imaging of defect structures AFM contact mode imaging using a sharp AFM probe was performed to examine the surface of the GO films deposited on a Si substrate. As Figure S1 shows, defect types such as island, fragment and hole were identified. Figure S1: AFM images of GO films deposited on a Si substrate showing defect types of (a) island, (b) fragment, and (c) hole. Height profiles were drawn along the red dash lines indicated in each figure. The grey lines roughly indicate flake edges. 1 These authors contributed equally.
2 2. Experimental mechanics model for interfacial shear strength (ISS) of GO Estimating the contact area is necessary for determining ISS from friction vs. normal force data. For the experimental setup used in this work, adhesion must be taken into account in the contact area calculation. Surface forces act over a spatial range, which relies on the chemistry of materials in contact. The forces may or may not be long range compared to the scale of elastic deformations. 1 Johnson-Kendall-Roberts (JKR) 1 and Derjaguin-Müller-Toporov (DMT) 2 models are two extreme cases. The JKR model only includes short range adhesion inside the contact region, while the DMT model considers long range adhesion outside the contact region only. The Maugis-Dugdale model introduces a parameter that can define the transition from JKR to DMT. 3 Carpick et al. 4 further developed a fitting procedure of the normal force versus friction force plot to facilitate the implementation of the JKR-DMT transition model. Following this procedure, coupled with a mechanics model of a coated rigid sphere in contact with another rigid coated substrate, 5 the ISS can be calculated. Based on the JKR-DMT transition model, 3, 4 ISS is a function of the pull-off force and the contact radius: = (1) where τ is the ISS, F0 is the pull-off force, and a is the contact radius. Following Carpick et al s 4 fitting procedure, a can be expressed as = (2) where is the contact radius at zero load as a function of the Maugis non-dimensional unit λ defining the transition point between JKR and DMT models, K is the reduced modulus of two contact bodies, γ is the work of adhesion, and R is the AFM tip radius (in the current work the radius of the silica sphere which was measured by SEM imaging to be ~15 µm). By fitting the normal load vs. friction force curve, F0, λ, and γ can be determined. 4 In terms of the reduced modulus K, this study is different from the more common situation where a standard sharp AFM tip directly contacts a solid substrate because the spherical tip and the Si substrate were both coated with GO films. Hence, a proper model to calculate K is required. For a rigid sphere with coatings in contact with a rigid coated substrate the reduced modulus K can be estimated according to Reedy et al. 5 =h + (3) where h1 is the thickness of GO coating on the sphere, h2 is the thickness of GO coating on the Si substrate, h is the sum of h1 and h2, and Eu1 and Eu2 are the uniaxial strain moduli of two GO films, respectively (Figure 1). In the current work, the sphere was made of silica (E = 95.6 GPa) 6 and the substrate was Si (E = 170 GPa) 7 which were both considered as rigid bodies due to their high stiffness as compared to the GO films (E = 32 GPa), 8 Since the GO films on the sphere and the substrate were from the same GO solution, Young s moduli were assumed to be the same for both coated GO films. Thus, Eu1 and Eu2 are = = (4)
3 where, ν1 is Poisson s ratio (0.195), 9 and E is the Young s modulus (32 GPa). 8 In addition, given that h=h1+h2, Equation (3) simplifies to = =E 3. Atomic topologies of defect structures The initial topologies (i.e. prior to relaxation) for the H-100, F-100 and I-100 structures are provided in Figure S2. The dimensions of each defective structure are indicated in the figure. In order to obtain these initial topological structures, atoms were deleted or added as necessary from the P-100 model. In the case of the H-100 and I-100 defects, the features are not perfectly circular as an effort was made limit the number of dangling bonds. (5) Figure S2: The atomic topologies of the H-100 (a), F-100 (b) and I-100 (c) defect structures upon initialization. 4. Surface roughness and interfacial distance During relaxation, undulations are observed to form in the GO films. This behavior is consistent with previous molecular dynamics (MD) 10, 11, 12 and density functional theory studies (DFT). 13 These undulations cause variations in the interlayer spacing (h) and induce surface roughness effects. In the current work, roughness ( ) was calculated using the following relation:
4 = (6) where is the average height of atoms in the carbon plane and represents individual height measurements. of the experimental dataset may also be determined in a similar manner from application of Equation (6) against the collected AFM linescans. The roughness measurement for each experimental and MD dataset are provided in Tables S1 and S2. In experimental measurements, was determined from AFM linescans at the lowest contact load (200 nn). A strong correlation between and ISS was not observed for the experimental data. For MD simulations, was calculated from the relaxed topologies prior to shear deformation. The interlayer spacing may also be determined from the atomic position information by subtracting the values of adjacent graphene layers. This data is also provided in Table S2 for each MD topology. The order of magnitude differences in roughness between experimental and computational datasets are the major contributing factor to differences in ISS measurements. Roughness was not calculated for the interlayer registry variation study as all rotated preparations were of a P-100 preparation. Table S1: Roughness and corresponding ISS measurements for the experimental dataset. Data (nm) ISS (MPa) Table S2: Roughness, interlayer spacing, and ISS for the MD dataset. Functional structure variation Topological defect variation P-100 P-75 P-50 P-25 P-100 F-100 H-100 I-100 (nm) h (Å) ISS (MPa) The effect of sliding rate on ISS Since deformation events in defective graphene structures are known to be sensitive to loading rate, 14, 15 the influence of sliding rate on the ISS was investigated. Figure S3 presents the ISS measurements for the P-100 topology at effective displacements of ~2, 10, and 20 m/s. The error bars represent a 95% confidence interval (n = 5). As shown in the figure, the ISS was found to be insensitive to the loading rates examined in this study.
5 Figure S3: The influence of loading rate on ISS for the P-100% topology. Error bars represent a 95% confidence interval (n = 5). 6. Influence of the number of displaced layers and number of layers in the MD supercell on the ISS The number of layers selected to be displaced was varied in order to assess the influence on the ISS. Figure S4 presents the shear response of a P-100% topology with a single layer displaced and with two layers displaced (as in the main text). The results appear to be consistent. Additionally, Figure S5 shows results for MD simulations of a P-100% topology with 4 and 5 layers in the supercell. In all parametric scenarios, there does not appear to be a significant effect on the ISS. Figure S4: Shear responses of P-100% topologies with single and two layer slip.
6 Figure S5: Shear responses of P-100% topologies with four and five layers in the MD supercell. References 1. Johnson, K. L.; Greenwood, J. A., An Adhesion Map for the Contact of Elastic Spheres. Journal of Colloid and Interface Sciences 1997, 192 (2), Derjaguin, B. V.; Muller, V. M.; Toporov, Y. P., Effect of contact deformations on the adhesion of particles. Progress in Surface Science 1994, 45 (1-4), Maugis, D., Adhesion of spheres: The JKR-DMT transition using a dugdale model. Journal of Colloid and Interface Sciences 1992, 150, Carpick, R. W.; Ogletree, D. F.; Salmeron, M., A General Equation for Fitting Contact Area and Friction vs Load Measurements. Journal of Colloid and Interface Science 1999, 211 (2), Reedy, E. D., Contact mechanics for coated spheres that includes the transition from weak to strong adhesion. Journal of Materials Research 2007, 22 (9), Pabst, W.; Gregorová, E., Elastic properties of silica polymorphs-a review. Ceramics - Silikaty 2013, 57 (3), Sharpe, W. N.; Jackson, K. M.; Hemker, K. J.; Xie, Z., Effect of specimen size on Young's modulus and fracture strength of polysilicon. Journal of Microelectromechanical Systems 2001, 10 (3), Dikin, D. A.; Stankovich, S.; Zimney, E. J.; Piner, R. D.; Dommett, G. H. B.; Evmenenko, G.; Nguyen, S. T.; Ruoff, R. S., Preparation and characterization of graphene oxide paper. Nature 2007, 448 (7152), Peng, Q.; De, S., Mechanical properties and instabilities of ordered graphene oxide C6O monolayers. RSC Advances 2013, 3 (46), Compton, O. C.; Cranford, S. W.; Putz, K. W.; An, Z.; Brinson, L. C.; Buehler, M. J.; Nguyen, S. T., Tuning the Mechanical Properties of Graphene Oxide Paper and Its Associated Polymer Nanocomposites by Controlling Cooperative Intersheet Hydrogen Bonding. ACS Nano 2012, 6 (3), Medhekar, N. V.; Ramasubramaniam, A.; Ruoff, R. S.; Shenoy, V. B., Hydrogen Bond Networks in Graphene Oxide Composite Paper: Structure and Mechanical Properties. ACS Nano 2010, 4 (4), Cao, C.; Daly, M.; Chen, B.; Filleter, T.; Singh, C. V.; Sun, Y., Strengthening in graphene oxide nanosheets: Bridging the gap between interplanar and intraplanar fracture. Nano Letters 2015, 15 (10)
7 13. Kim, S.; Zhou, S.; Hu, Y.; Acik, M.; Chabal, Y. J.; Berger, C.; de Heer, W.; Bongiorno, A.; Riedo, E., Room-temperature metastability of multilayer graphene oxide films. Nature Materials 2012, 11 (6), Daly, M.; Singh, C. V., A kinematic study of energy barriers for crack formation in graphene tilt boundaries. Journal of Applied Physics 2014, 115 (22), Daly, M.; Reeve, M.; Singh, C. V., Effects of topological point reconstructions on the fracture strength and deformation mechanisms of graphene. Computational Materials Science 2015, 97,
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